There is well known an automatic transmission which comprises a plurality of coupling devices for transmitting a rotary motion and a torque between an input shaft provided to receive a drive force from a drive power source and an output shaft provided to transmit the drive force to drive wheels. The automatic transmission is configured to be shifted with concurrently performed engaging and releasing actions of the respective two coupling devices. Generally, the automatic transmission of this type is shifted according to manipulated amounts, i.e., control inputs determined by a control map obtained for each shift position by simulation on an actual vehicle wherein required values (namely, the manipulated amounts, i.e., control inputs) of control parameters (such as torque values) of devices to be controlled for shifting actions are optimized for each shift position. However, a recent demand for an increase of the required number of shift positions of an automatic transmission causes a need for a considerably large amount of efforts for optimization of the manipulated amounts, making it difficult to adopt a shifting control mode based on the control map. In view of this difficulty, there has been proposed a shifting model control which is a shifting control mode based on motion equations for each of rotary elements incorporated in the automatic transmission. In this shifting model control, the automatic transmission is shifted according to manipulated amounts uniquely determined by solving the motion equations obtained on the basis of a required manner of change (shifting target values) for each shifting action. For instance, Patent Document 1 discloses a technique for implementing a shifting control of the automatic transmission wherein a target value of a rotating speed of an input shaft of the automatic transmission is determined as one of the shifting target values during an inertia phase control, while a required value of a torque of a clutch to be engaged is calculated as one of the manipulated amounts according to a shifting model. The Patent Document 1 further discloses a technique for implementing a shifting control of the automatic transmission wherein target values of the rotating speed of the input shaft and a torque of an output shaft of the automatic transmission are determined as the shifting target values, while a required value of a torque of a clutch to be engaged and a required value of a torque of a clutch to be released are calculated as the manipulated amounts according to a shifting model.